The rupee declined by 21 paise to trade at fresh one-month low of 60.80 against the US dollar in early trade on Tuesday due to appreciation of the American unit against other currencies overseas.
Besides, an increased demand for the US dollar from importers also put pressure on the rupee.
The local unit had lost 30 paise to close at one-month low of 60.59 against the dollar on Monday due to fresh demand for the US currency from importers, mainly oil refiners.
Dealers attributed the fall in the rupee today to dollar's gains against other currencies overseas, but a higher opening in the domestic equity market capped the fall.
Meanwhile, the benchmark BSE Sensex rose by 47.53 points, or 0.20%, to hit an all-time high of 22,812.36 in opening trade on Tuesday.